%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP612-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 12:57:21 EDT 2022
% Result : Unsatisfiable 1.70s 1.95s
% Output : Refutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of clauses : 34 ( 34 unt; 0 nHn; 4 RR)
% Number of literals : 34 ( 33 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 86 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(a,b) != multiply(b,a),
file('GRP612-1.p',unknown),
[] ).
cnf(2,plain,
multiply(b,a) != multiply(a,b),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(4,axiom,
inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,C))) = B,
file('GRP612-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = inverse(double_divide(B,A)),
file('GRP612-1.p',unknown),
[] ).
cnf(8,plain,
inverse(double_divide(A,B)) = multiply(B,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,flip.1')] ).
cnf(9,plain,
multiply(double_divide(A,B),multiply(B,multiply(C,A))) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4]),8,8,8]),
[iquote('back_demod,4,demod,8,8,8')] ).
cnf(11,plain,
multiply(double_divide(multiply(A,multiply(B,C)),D),multiply(D,B)) = double_divide(C,A),
inference(para_into,[status(thm),theory(equality)],[9,9]),
[iquote('para_into,9.1.1.2.2,9.1.1')] ).
cnf(13,plain,
multiply(double_divide(multiply(A,B),double_divide(B,C)),A) = C,
inference(para_into,[status(thm),theory(equality)],[9,9]),
[iquote('para_into,9.1.1.2,9.1.1')] ).
cnf(35,plain,
double_divide(A,multiply(double_divide(multiply(B,A),C),B)) = C,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[11,13])]),
[iquote('para_into,11.1.1,13.1.1,flip.1')] ).
cnf(66,plain,
multiply(double_divide(multiply(A,multiply(B,C)),D),A) = double_divide(C,multiply(D,B)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[35,35])]),
[iquote('para_into,35.1.1.2.1,35.1.1,flip.1')] ).
cnf(67,plain,
double_divide(multiply(A,B),double_divide(B,multiply(C,A))) = C,
inference(para_into,[status(thm),theory(equality)],[35,11]),
[iquote('para_into,35.1.1.2,11.1.1')] ).
cnf(77,plain,
inverse(A) = multiply(multiply(double_divide(multiply(B,C),A),B),C),
inference(para_from,[status(thm),theory(equality)],[35,8]),
[iquote('para_from,35.1.1,7.1.1.1')] ).
cnf(79,plain,
multiply(multiply(double_divide(multiply(A,B),C),A),B) = inverse(C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[77])]),
[iquote('copy,77,flip.1')] ).
cnf(101,plain,
inverse(A) = multiply(double_divide(B,multiply(A,C)),multiply(C,B)),
inference(para_from,[status(thm),theory(equality)],[67,8]),
[iquote('para_from,67.1.1,7.1.1.1')] ).
cnf(102,plain,
multiply(double_divide(A,multiply(B,C)),multiply(C,A)) = inverse(B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[101])]),
[iquote('copy,101,flip.1')] ).
cnf(129,plain,
multiply(double_divide(A,double_divide(A,multiply(B,C))),inverse(B)) = C,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[79,9]),66]),
[iquote('para_from,79.1.1,9.1.1.2,demod,66')] ).
cnf(232,plain,
double_divide(multiply(inverse(A),B),multiply(A,C)) = double_divide(B,C),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[129,35])]),
[iquote('para_from,129.1.1,35.1.1.2,flip.1')] ).
cnf(354,plain,
double_divide(multiply(A,multiply(inverse(B),C)),double_divide(C,A)) = B,
inference(para_from,[status(thm),theory(equality)],[232,67]),
[iquote('para_from,232.1.1,67.1.1.2')] ).
cnf(356,plain,
double_divide(A,multiply(double_divide(A,B),inverse(C))) = multiply(C,B),
inference(para_from,[status(thm),theory(equality)],[232,35]),
[iquote('para_from,232.1.1,35.1.1.2.1')] ).
cnf(368,plain,
double_divide(inverse(A),double_divide(B,double_divide(B,multiply(A,inverse(C))))) = C,
inference(para_into,[status(thm),theory(equality)],[354,102]),
[iquote('para_into,354.1.1.1,102.1.1')] ).
cnf(400,plain,
multiply(A,double_divide(B,multiply(A,C))) = double_divide(B,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[356,129])]),
[iquote('para_into,356.1.1.2,129.1.1,flip.1')] ).
cnf(429,plain,
multiply(A,double_divide(B,double_divide(C,D))) = double_divide(B,double_divide(C,multiply(A,D))),
inference(para_into,[status(thm),theory(equality)],[400,400]),
[iquote('para_into,400.1.1.2.2,400.1.1')] ).
cnf(440,plain,
double_divide(A,double_divide(B,double_divide(B,multiply(C,D)))) = double_divide(A,multiply(C,D)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[400,11]),429,66]),
[iquote('para_into,400.1.1.2.2,11.1.1,demod,429,66')] ).
cnf(472,plain,
double_divide(inverse(A),multiply(A,inverse(B))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[368]),440]),
[iquote('back_demod,368,demod,440')] ).
cnf(522,plain,
multiply(A,B) = double_divide(inverse(A),inverse(B)),
inference(para_from,[status(thm),theory(equality)],[472,400]),
[iquote('para_from,472.1.1,400.1.1.2')] ).
cnf(526,plain,
double_divide(multiply(inverse(A),inverse(B)),A) = B,
inference(para_from,[status(thm),theory(equality)],[472,67]),
[iquote('para_from,472.1.1,67.1.1.2')] ).
cnf(564,plain,
double_divide(inverse(b),inverse(a)) != multiply(a,b),
inference(para_from,[status(thm),theory(equality)],[522,2]),
[iquote('para_from,522.1.1,2.1.1')] ).
cnf(573,plain,
double_divide(multiply(inverse(multiply(A,B)),inverse(C)),B) = multiply(A,C),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[526,400])]),
[iquote('para_from,526.1.1,400.1.1.2,flip.1')] ).
cnf(577,plain,
multiply(A,multiply(B,inverse(A))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[526,13]),8]),
[iquote('para_from,526.1.1,13.1.1.1,demod,8')] ).
cnf(586,plain,
double_divide(A,double_divide(A,multiply(B,C))) = multiply(B,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[577,129])]),
[iquote('para_into,577.1.1.2,129.1.1,flip.1')] ).
cnf(599,plain,
multiply(multiply(A,B),inverse(A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[129]),586]),
[iquote('back_demod,129,demod,586')] ).
cnf(657,plain,
double_divide(multiply(inverse(multiply(A,B)),C),B) = double_divide(C,inverse(A)),
inference(para_from,[status(thm),theory(equality)],[599,232]),
[iquote('para_from,599.1.1,232.1.1.2')] ).
cnf(664,plain,
double_divide(inverse(A),inverse(B)) = multiply(B,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[573]),657]),
[iquote('back_demod,573,demod,657')] ).
cnf(665,plain,
$false,
inference(binary,[status(thm)],[664,564]),
[iquote('binary,664.1,564.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP612-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 05:24:44 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.70/1.95 ----- Otter 3.3f, August 2004 -----
% 1.70/1.95 The process was started by sandbox on n029.cluster.edu,
% 1.70/1.95 Wed Jul 27 05:24:44 2022
% 1.70/1.95 The command was "./otter". The process ID is 17707.
% 1.70/1.95
% 1.70/1.95 set(prolog_style_variables).
% 1.70/1.95 set(auto).
% 1.70/1.95 dependent: set(auto1).
% 1.70/1.95 dependent: set(process_input).
% 1.70/1.95 dependent: clear(print_kept).
% 1.70/1.95 dependent: clear(print_new_demod).
% 1.70/1.95 dependent: clear(print_back_demod).
% 1.70/1.95 dependent: clear(print_back_sub).
% 1.70/1.95 dependent: set(control_memory).
% 1.70/1.95 dependent: assign(max_mem, 12000).
% 1.70/1.95 dependent: assign(pick_given_ratio, 4).
% 1.70/1.95 dependent: assign(stats_level, 1).
% 1.70/1.95 dependent: assign(max_seconds, 10800).
% 1.70/1.95 clear(print_given).
% 1.70/1.95
% 1.70/1.95 list(usable).
% 1.70/1.95 0 [] A=A.
% 1.70/1.95 0 [] inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,C)))=B.
% 1.70/1.95 0 [] multiply(A,B)=inverse(double_divide(B,A)).
% 1.70/1.95 0 [] multiply(a,b)!=multiply(b,a).
% 1.70/1.95 end_of_list.
% 1.70/1.95
% 1.70/1.95 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.70/1.95
% 1.70/1.95 All clauses are units, and equality is present; the
% 1.70/1.95 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.70/1.95
% 1.70/1.95 dependent: set(knuth_bendix).
% 1.70/1.95 dependent: set(anl_eq).
% 1.70/1.95 dependent: set(para_from).
% 1.70/1.95 dependent: set(para_into).
% 1.70/1.95 dependent: clear(para_from_right).
% 1.70/1.95 dependent: clear(para_into_right).
% 1.70/1.95 dependent: set(para_from_vars).
% 1.70/1.95 dependent: set(eq_units_both_ways).
% 1.70/1.95 dependent: set(dynamic_demod_all).
% 1.70/1.95 dependent: set(dynamic_demod).
% 1.70/1.95 dependent: set(order_eq).
% 1.70/1.95 dependent: set(back_demod).
% 1.70/1.95 dependent: set(lrpo).
% 1.70/1.95
% 1.70/1.95 ------------> process usable:
% 1.70/1.95 ** KEPT (pick-wt=7): 2 [copy,1,flip.1] multiply(b,a)!=multiply(a,b).
% 1.70/1.95
% 1.70/1.95 ------------> process sos:
% 1.70/1.95 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.70/1.95 ** KEPT (pick-wt=14): 4 [] inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,C)))=B.
% 1.70/1.95 ---> New Demodulator: 5 [new_demod,4] inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,C)))=B.
% 1.70/1.95 ** KEPT (pick-wt=8): 7 [copy,6,flip.1] inverse(double_divide(A,B))=multiply(B,A).
% 1.70/1.95 ---> New Demodulator: 8 [new_demod,7] inverse(double_divide(A,B))=multiply(B,A).
% 1.70/1.95 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.70/1.95 >>>> Starting back demodulation with 5.
% 1.70/1.95 >>>> Starting back demodulation with 8.
% 1.70/1.95 >> back demodulating 4 with 8.
% 1.70/1.95 >>>> Starting back demodulation with 10.
% 1.70/1.95
% 1.70/1.95 ======= end of input processing =======
% 1.70/1.95
% 1.70/1.95 =========== start of search ===========
% 1.70/1.95
% 1.70/1.95
% 1.70/1.95 Resetting weight limit to 13.
% 1.70/1.95
% 1.70/1.95
% 1.70/1.95 Resetting weight limit to 13.
% 1.70/1.95
% 1.70/1.95 sos_size=273
% 1.70/1.95
% 1.70/1.95 -------- PROOF --------
% 1.70/1.95
% 1.70/1.95 ----> UNIT CONFLICT at 0.02 sec ----> 665 [binary,664.1,564.1] $F.
% 1.70/1.95
% 1.70/1.95 Length of proof is 30. Level of proof is 19.
% 1.70/1.95
% 1.70/1.95 ---------------- PROOF ----------------
% 1.70/1.95 % SZS status Unsatisfiable
% 1.70/1.95 % SZS output start Refutation
% See solution above
% 1.70/1.95 ------------ end of proof -------------
% 1.70/1.95
% 1.70/1.95
% 1.70/1.95 Search stopped by max_proofs option.
% 1.70/1.95
% 1.70/1.95
% 1.70/1.95 Search stopped by max_proofs option.
% 1.70/1.95
% 1.70/1.95 ============ end of search ============
% 1.70/1.95
% 1.70/1.95 -------------- statistics -------------
% 1.70/1.95 clauses given 27
% 1.70/1.95 clauses generated 597
% 1.70/1.95 clauses kept 448
% 1.70/1.95 clauses forward subsumed 333
% 1.70/1.95 clauses back subsumed 0
% 1.70/1.95 Kbytes malloced 4882
% 1.70/1.95
% 1.70/1.95 ----------- times (seconds) -----------
% 1.70/1.95 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.70/1.95 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.70/1.95 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.70/1.95
% 1.70/1.95 That finishes the proof of the theorem.
% 1.70/1.95
% 1.70/1.95 Process 17707 finished Wed Jul 27 05:24:46 2022
% 1.70/1.95 Otter interrupted
% 1.70/1.95 PROOF FOUND
%------------------------------------------------------------------------------